15.2. Refer to the previous exercise. When the explanatory variables are x1 = family income, x2 = number of years of education, and s = sex (1 = male, 0 = female), the prediction equation is logit[ˆP(y = 1)] = −2.40 + 0.03x1 + 0.05x2 + 0.40s.

For this sample, x1 ranges from 6 to 157 with a standard deviation of 25, and x2 ranges from 7 to 20 with a standard deviation of 3.

(a) Find the estimated probability of voting for Candidate X for (i) a man with 10 years of education and income

$50,000, (ii) a woman with 10 years of education and income $50,000.

(b) Convert the probabilities in

(a) to odds, and find the odds ratio, the odds for men divided by the odds for females.

Interpret.

(c) Show how the odds ratio in

(b) relates to the sex effect in the prediction equation.

(d) Holding the other variables constant, find the estimated effect on the odds of voting the candidate of (i) a standard deviation change in x2, (ii) a standard deviation change in x1. Which explanatory variable has the larger standardized effect? Interpret.